Several high-precision physics experiments are approaching a level of sensitivity at which the intrinsic quantum nature of the experimental apparatus is the dominant source of fluctuations limiting the sensitivity of the measurements. This quantum limit is embodied by the Heisenberg uncertainty principle, which prohibits arbitrarily precise simultaneous measurements of two conjugate observables of a system but allows one-time measurements of a single observable with any precision. The dynamical evolution of a system immediately following a measurement limits the class of observables that may be measured repeatedly with arbitrary precision, with the influence of the measurement apparatus on the system being confined strictly to the conjugate observables. Observables having this feature, and the corresponding measurements performed on them, have been named quantum nondemolition or back-action evasion observables. In a previous review (Caves et al., 1980, Rev. Mod. Phys. 52, 341) a quantum-mechanical analysis of quantum nondemolition measurements of a harmonic oscillator was presented. The present review summarizes the experimental progress on quantum nondemolition measurements and the classical models developed to describe and guide the development of practical implementations of quantum nondemolition measurements. The relationship between the classical and quantum theoretical models is also reviewed. The concept of quantum nondemolition and back-action evasion measurements originated in the context of measurements on a macroscopic mechanical harmonic oscillator, though these techniques may be useful in other experimental contexts as well, as is discussed in the last part of this review. [S0034-6861(96)00103-1] CONTENTS

The compressed sensing (CS)

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The vacuum tunneling probe used in the scanning tunneling microscope represents a new class of nonreciprocal electromechanical transducers. Nonreciprocity implies reduced back action and consequently increased sensitivity over conventional, reciprocal transducers. A vacuum tunneling probe may reach the quantum limit for a measurement of the position of a macroscopic mechanical oscillator even with use of a non-quantum-limited amplifier. The quantum limit is enforced by the momentum shot noise associated with the tunneling current.

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We investigate the effects of different levels of delay (or latency) on the coordination, pace and timing regularity of musicians who are in remote locations—a situation encountered in an interactive network performance. Two pairs of musicians performed two Mozart duets while isolated visually and connected through microphones and headphones. Different levels of latency (0, 20, 40, 50, 80, 100, 120, 150, and 200 ms) were introduced into the performing environment (musicians heard themselves in real time and only the other part delayed); the musicians performed the duets under these conditions and rated their musicality and level of interactivity. Although the musicians chose different strategies to handle the latency, which resulted in different levels of success in maintaining coordination, pacing and regularity, both duets were strongly affected by latency at and above 100 ms. At these levels, the musicians rated the performances as neither musical nor interactive, and they reported that they played as individuals and listened less and less to one another.

The fundamental sources of noise in a vacuum-tunneling probe used as an electromechanical transducer to monitor the location of a test mass are examined using a first-quantization formalism. We show that a tunneling transducer enforces the Heisenberg uncertainty principle for the position and momentum of a test mass monitored by the transducer through the presence of two sources of noise: the shot noise of the tunneling current and the momentum fluctuations transferred by the tunneling electrons to the test mass. We analyze a number of cases including symmetric and asymmetric rectangular potential barriers and a barrier in which there is a constant electric field. Practical configurations for reaching the quantum limit in measurements of the position of macroscopic bodies with such a class of transducers are studied

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